Transverse instability of plane wavetrains in gas-fluidized beds

摘要: Using a two-fluid model of gas-fluidized beds, it is shown that periodic plane voidage waves travelling against gravity are unstable to perturbations with large transverse wavelength. This secondary instability sets in at arbitrarily small amplitudes the wave and correspondingly wavenumbers two-dimensional perturbation. More precisely, if bed wide enough accommodate sufficiently long horizontal waves, then becomes as soon its amplitude has grown order square wavenumber. The can be stationary or oscillatory nature origin interaction between four least-stable modes Two them represent pair bubble-like ‘mixed modes‘; other two initially, i. e. onset primary wave, pure modes, one consisting only an initially vertical velocity perturbation state uniform fluidization. Depending on relation eigenvalues bifurcation point, either these dominant mode, which (most) along growing vertically wave. While gain longitudinal structure during this process, mixed obtain component averaged well, so appears described here variant Batchelor & Nitsche's (1991) ‘overturning’ found recently for unbounded stratified fluids, see also (1993).